Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Polynomial decomposition algorithms
Journal of Symbolic Computation
Functional decomposition ofpolynomials: the tame case
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Functional decomposition of polynomials: The wild case
Journal of Symbolic Computation
On multivariate rational function decomposition
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Algebraic Methods for Constructing Asymmetric Cryptosystems
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Asymmetric cryptography with S-Boxes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Cryptoanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Analytic models for token-ring networks
Analytic models for token-ring networks
The functional decomposition of polynomials
The functional decomposition of polynomials
Cryptanalysis of Patarin's 2-round public key system with S boxes (2R)
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
High order derivatives and decomposition of multivariate polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Interactions between computer algebra (Gröbner bases) and cryptology
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Decomposition of generic multivariate polynomials
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
On multivariate homogeneous polynomial decomposition
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Linear recurring sequences for the UOV key generation
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
| Hi-index | 0.00 |
In this paper, we present an efficient and general algorithm for decomposing multivariate polynomials of the same arbitrary degree. This problem, also known as the Functional Decomposition Problem (FDP), is classical in computer algebra. It is the first general method addressing the decomposition of multivariate polynomials (any degree, any number of polynomials). As a byproduct, our approach can be also used to recover an ideal I from its kth power I^k. The complexity of the algorithm depends on the ratio between the number of variables (n) and the number of polynomials (u). For example, polynomials of degree four can be decomposed in O(n^1^2), when this ratio is smaller than 12. This work was initially motivated by a cryptographic application, namely the cryptanalysis of 2R^- schemes. From a cryptographic point of view, the new algorithm is so efficient that the principle of two-round schemes, including 2R^- schemes, becomes useless. Besides, we believe that our algorithm is of independent interest.